Hydrogen free amorphous silicon as insulating dielectric material for superconducting quantum bits

ABSTRACT

A hydrogen-free amorphous dielectric insulating film having a high material density and a low density of tunneling states. The film is prepared by deposition of a dielectric material on a substrate having a high substrate temperature T sub  under high vacuum and at a controlled low deposition rate. In one embodiment, the film is amorphous silicon while in another embodiment the film is amorphous germanium.

CROSS-REFERENCE

This application is a Continuation-in-Part of, and claims the benefit ofpriority under 35 U.S.C. §120 based on U.S. patent application Ser. No.14/538,968 filed on Nov. 12, 2014, which is a Nonprovisional of, andclaims the benefit of priority under 35 U.S.C. §119 based on, U.S.Provisional Patent Application No. 61/903,521 filed on Nov. 13, 2013.The prior applications and all references cited herein are herebyincorporated by reference into the present application.

TECHNICAL FIELD

The present invention relates to amorphous thin film materials such asamorphous silicon (a-Si), amorphous germanium (a-Ge), amorphous carbon(a-C) that are free from two-level tunneling systems (TLS) and aresuitable for use as an insulating dielectric material for supercomputingquantum bits.

BACKGROUND

Quantum computing has been a rapidly developing research field in thepast two decades. At the heart of quantum computing is the quantum bit,or qubit. The qubit is a unit of quantum information, the quantumanalogue of the classical bit in our current computer systems. Qubits ina quantum computer must be able to retain the quantum information theyare given long enough to perform quantum logic operations with them.

In principle, any two-level quantum system can be used as a qubit. Awide range of candidate quantum systems have been studied for theirpossible implementation in practical quantum computer as qubits. Theycan be photons, electrons or nuclear spins, trapped atoms or ions,defect quantum states in solids, superconducting circuits (Josephsonjunctions), etc.

Superconducting circuits with Josephson junction are solid state devicesfabricated by modern integrated circuits techniques, and are manipulatedand measured by well-developed low frequency electronics and microwavetechniques. A Josephson junction is formed by connecting twosuperconducting electrodes separated by a dielectric insulating layer. Agroup of qubits that are based on superconducting circuits involvesnanofabricated superconducting electrodes coupled through Josephsonjunctions. Such systems are one of the most promising systems for beingfully electronic and easily scalable for large arrays of qubits. See M.Steffan, “Superconducting Qubits Are Getting Serious,” Physics 4, 103(2011).

There are many different ways to build a qubit, each having its own prosand cons. Superconducting circuits with Josephson junctions have emergedas a promising technology for quantum information processing withsolid-state devices for its scalability, in which superconductor isassembled macroscopically to form qubits. Since such qubits involve thecollective motion of a large number (˜10¹⁰) of Cooper-pair electrons,the coherence time is typically very short. Progress has been made toincrease the coherence time from 1 ns in 1999 to 60 μs in 2011. SeeSteffan, supra. It is now understood that dielectric loss from two-levelstates in the dielectric insulating layer is the dominant decoherencesource in superconducting qubits. See J. M. Martinis, K. B. Cooper, R.McDermott, Matthias Steffen, M. Ansmann, K. D. Osborn, K. Cicak, S. Oh,D. P. Pappas, R. W. Simmonds, and C. C. Yu, “Decoherence in JosephsonQubits from Dielectric Loss,” Phys. Rev. Lett., 95, 210503 (2005). Thesolution will be either to reduce TLS in dielectric layer or to minimizetheir impact by other means.

Currently, the main issue that limits the performance of superconductingqubits is the decoherence caused by spurious coupling of qubits tomicroscopic defect states in the materials used to implement thecircuits. Dielectric loss from the two-level tunneling systems (TLS) inthe amorphous dielectric thin films used as insulating layers is thedominant source of decoherence. See Martinis, supra. TLS universallyexist in almost all kinds of amorphous solids and a large number ofdisordered crystalline solids. R. O. Pohl, X. Liu, and E. J. Thompson,“Low temperature thermal conductivity and acoustic attenuation inamorphous solids,” Rev. of Mod. Phys. 74, 991 (2002). A special type ofhydrogenated amorphous silicon prepared by hot-wire chemical vapordeposition was found to contain almost no TLS. See X. Liu, B. E. White,Jr., R. O. Pohl, E. Iwanizcko, K. M. Jones, A. H. Mahan, B. N. Nelson,R. S. Crandall, and S. Veprek, “Amorphous solid without low energyexcitations,” Phys. Rev. Lett. 78, 4418 (1997) (“Liu 1997”). However,this material is difficult to prepare and the TLS content is hard tocontrol in a reproducible way. X. Liu and R. O. Pohl, “Low-energyexcitations in amorphous films of silicon and germanium”, Phys. Rev. B58, 9067 (1998) (“Liu 1998”).

Efforts have been made to reduce the density of TLS. Hydrogenatedsilicon nitride has been used to replace silicon dioxide as dielectriclayer and dielectric loss is reduced by a factor of 50. See H. Paik andK. D. Osborn, “Reducing quantum-regime dielectric loss of siliconnitride for superconducting quantum circuits,” Appl. Phys. Lett., 96,072505 (2010). Efforts have also been made to make overall device sizelarger while keeping the dielectric layer thickness as small as possibleto reduce the relative impact. See H. Paik, D. I. Schuster, L. S.Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J.Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, and R.J. Schoelkop, “Observation of High Coherence in Josephson JunctionQubits Measured in a Three-Dimensional Circuit QED Architecture,” Phys.Rev. Lett. 107, 240501 (2011). This has achieved the record longcoherence time of 60 μs. Of course, using completely crystalline siliconas dielectric layer has also being pursued with limited success assurface defect states become the main source of dielectric loss. See S.J. Weber, K. W. Murch, D. H. Slichter, R. Vijay, and I. Siddiqi, “Singlecrystal silicon capacitors with low microwave loss in the single photonregime,” Appl. Phys. Lett. 98, 172510 (2011).

SUMMARY

This summary is intended to introduce, in simplified form, a selectionof concepts that are further described in the Detailed Description. Thissummary is not intended to identify key or essential features of theclaimed subject matter, nor is it intended to be used as an aid indetermining the scope of the claimed subject matter. Instead, it ismerely presented as a brief overview of the subject matter described andclaimed herein.

The present invention provides hydrogen-free amorphous dielectricinsulating thin films having a low density of tunneling states and aprocess for making the same. The amorphous material comprising the filmshave a high mass density, typically at least 90% of the density of itscrystalline counterpart.

In an exemplary embodiment, a film in accordance with the presentinvention is an amorphous silicon film having a density greater thanabout 2.18 g/cm³ and a hydrogen content of less than about 0.1%,prepared by electron beam (e-beam) deposition at a controlled rate ofabout 0.1 nm/sec on a substrate having T_(sub)=400° C. under a vacuumpressure of 1×10⁻⁸ Torr. The film is prepared by deposition of adielectric material on a substrate having a high substrate temperatureT_(sub) just below the temperature at which the material exhibitscrystalline states, the deposition being in a high vacuum (low pressure)environment, e.g., about 1×10⁻⁷ to about 1×10⁻¹¹ Torr, and at acontrolled low deposition rate, e.g., less than about 0.1 nm/sec.

In another exemplary embodiment, a film in accordance with the presentinvention is an amorphous germanium (a-Ge) film having a thickness ofabout 330 nm and a hydrogen content of less than about 0.1%.

In accordance with the present invention, such an amorphous germaniumfilm can be prepared by e-beam deposition from a high-purity (99.9999%pure) Ge source on a substrate having a substrate temperature T_(sub) offrom room temperature to about 200° C. at a controlled growth rate ofabout 0.03 to about 0.05 nm/sec. Deposition is made in an ultra-highvacuum (UHV) environment with a base pressure of about 5×10⁻¹¹ Torr,with the pressure during film growth typically being at about at 5×10⁻⁹Torr.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 are plots depicting Raman spectra of e-beam a-Si films depositedat different growth temperatures.

FIGS. 2A-2D are cross-sectional transmission electron microscope (TEM)images of e-beam a-Si films deposited at T_(sub)=45° C. and 400° C.

FIG. 3 shows plots of specific heat plotted as C/T³ versus temperature Tfor e-beam a-Si films prepared at three different substrate temperaturesT_(sub).

FIG. 4 is a plot of internal friction versus temperature T for e-beama-Si films prepared at four different substrate temperatures T_(sub).

FIG. 5 is a plot of the relative changes of the speed of sound versustemperature T for e-beam a-Si films prepared at four different substratetemperatures T_(sub).

FIG. 6 is a plot showing, the TLS density no versus film density n_(Si),the TLS density no from the film specific heat C, and the spectral TLSdensity P from the film internal friction for e-beam a-Si films preparedat four different substrate temperatures T_(sub).

FIG. 7 is a plot showing Raman spectra of thin Ge films prepared at roomtemperature (RT), 120° C., 160° C., and 200° C.

FIG. 8 is a plot showing measurements of internal friction for a typicalamorphous solid (a-SiO₂) and for thin Ge films prepared at substratetemperatures of 7.5° C., 120° C., 160° C., and 200° C.

FIG. 9 shows the relative change of speed of sound of the same filmsshown in FIG. 8 measured at the same time as the internal friction.

DETAILED DESCRIPTION

The aspects and features of the present invention summarized above canbe embodied in various forms. The following description shows, by way ofillustration, combinations and configurations in which the aspects andfeatures can be put into practice. It is understood that the describedaspects, features, and/or embodiments are merely examples, and that oneskilled in the art may utilize other aspects, features, and/orembodiments or make structural and functional modifications withoutdeparting from the scope of the present disclosure.

All references cited herein are incorporated into the present disclosurein their entirety.

As noted above, it is desirable to obtain a high-quality insulatingdielectric material that is free from TLS for use with superconductingquantum bits. Such a TLS-free material can be used as the insulatingdielectric layer to separate the two superconducting layers in aJosephson junction without producing undesirable dielectric losses anddecoherence in the supercomputing qubits.

It has previously been thought that hydrogen incorporation in amorphoussilicon was important to eliminate TLS. However, in practice, it is hardto control the right amount of hydrogen, and the presence of hydrogencan often do more harm than good in such a material. The inventors ofthe present invention have demonstrated that increasing mass densityreduces TLS density in several different amorphous solids, and thathydrogen is not a necessary ingredient to reduce TLS in amorphoussolids. See D. R. Queen, X. Liu, J. Karel, H. C. Jacks, T. H. Metcalf,and F. Hellman, “Two-level systems in evaporated amorphous silicon,” J.Non-Cryst. Solids, 426, 19-24 (2015). The inventors of the presentinvention have also recently discovered that amorphous silicon (a-Si)thin films produced by electron beam (e-beam) evaporation on substrateshaving a high substrate temperature T_(sub) are high density films thatcontain no TLS. See X. Liu, D. Queen, T. H. Metcalf, J. E. Karel, and F.Hellman, “Hydrogen free amorphous silicon with no tunneling states,”Phys. Rev. Lett. 113, 025503 (2014) (“Liu 2014”); and D. R. Queen, X.Liu, J. Karel, T. H. Metcalf, and F. Hellman, “Excess specific heat inevaporated amorphous silicon,” Phys. Rev. Lett., 110, 135901 (2013).

Thus, the present invention includes high-density hydrogen-freeamorphous dielectric insulating thin films that are substantially freefrom two-level tunneling systems (TLS) and a process for forming thesame. The amorphous material comprising the films have a high massdensity close to that of its crystalline counterpart, typically having adensity of at least 90% of the density of its crystalline counterpart.For example, a-Si prepared in accordance with the process of the presentinvention has a mass density of about 2.18 g/cm³, compared to a massdensity of about 2.329 g/cm³ for Si in its crystalline form.

Such material is a perfect candidate for use as a dielectric insulatinglayer in superconducting qubits. Specific heat measurements of a-Si madeby the inventors show that the density of TLS is reduced by a factor of100 as the substrate temperature T_(sub) increases from 45° C. to 400°C. In addition, the inventors found that the elastic loss, or internalfriction, of this a-Si material is about three orders of magnitudesmaller than that of a typical amorphous thin film.

In an exemplary embodiment, the TLS-free insulating dielectric thinfilms provided by the present invention are in the form of a-Si thinfilms having a mass density greater than about 2.18 g/cm³ and a hydrogencontent of less than about 0.1%. In other embodiments, the TLS-freeinsulating dielectric thin films in accordance with the presentinvention can include high-density amorphous germanium (a-Ge) oramorphous carbon (a-C), while in still other embodiments, the thin filmmay be a compound or alloy film formed from at least two elements, forexample, from two or more of silicon (Si), germanium (Ge), carbon (C),nitrogen (N), phosphorus (P), arsenic (As), boron (B), aluminum (Al),gallium (Ga), or oxygen (O).

Irrespective of the materials used, because the amorphous dielectricinsulating thin films according to the present invention do not containtwo-level tunneling systems, they are particularly well-suited forsuperconducting qubits, Josephson junctions, and other devices wherenoise from two-level systems degrades performance.

Such high-density TLS-free amorphous dielectric insulating thin filmsare obtained by depositing an insulating dielectric material on asubstrate having a high substrate temperature T_(sub) just below atemperature at which the material will begin to exhibit crystallinestates. Deposition will often be by electron beam (e-beam) evaporationof the material on the substrate, though any other suitable depositiontechnique such as sputtering, chemical vapor deposition, or pulsed laserdeposition may also be used. Deposition will typically start in a highbase vacuum (low pressure) environment, e.g., about 1×10⁻⁷ to about1×10⁻¹¹ Torr, at a controlled slow deposition rate, e.g., about 0.1nm/sec.

Thus, in an exemplary embodiment, a process for preparing a TLS-freedielectric insulating thin film in accordance with the present inventionincludes the steps of depositing Si on a substrate having a substratetemperature T_(sub) of about 350° C. to about 400° C. using e-beamevaporation under a vacuum pressure of about 1×10⁻⁸ Torr at a rate ofabout 1 Å (0.1 nm) per second Of course, in other embodiments, otherappropriate vacuum pressures and/or deposition rates may be used toproduce TLS-free amorphous dielectric insulating thin films from Si orother appropriate materials, and all such other embodiments are deemedto be within the scope of the present invention.

To investigate the properties of exemplary TLS-free amorphous dielectricinsulating thin films in accordance with the present invention, theinventors prepared a-Si thin films by e-beam evaporation from a highpurity Si source in a UHV system on substrates having a substratetemperature T_(sub) varying from 45° C. to 400° C. with a base pressureof 1×10⁻⁸ Torr and a growth rate of 0.05-0.1 nm/sec.

Films grown on the substrates at the same time or in identicalconditions were examined by Raman spectroscopy and X-ray diffraction,and all films were found to be fully amorphous. The Raman spectra,measured with the 514.5 nm line of an Ar ion laser, of the a-Si filmsdeposited using e-beam deposition at T_(sub)=45, 200, and 400° C. areshown in FIG. 1. These spectra show two distinct bands, a first band at200 cm⁻¹ and a second band at about 480 cm⁻¹, where the first and secondbands are associated with transverse-acoustic (TA) andtransverse-optical (TO) vibrational modes, respectively. Also shown inFIG. 1 are the longitudinal-acoustic (LA) and longitudinal-optical (LO)modes between 200 and 420 cm⁻¹. As can be seen from the plots in FIG. 1,the TO peak narrows and sharpens with increasing T_(sub), indicating aprogressive reduction of the RMS bond angles deviation of a-Si shown inthe inset. At the same time, the difference in intensity between the TAand TO peaks decreases, indicating an increase in the intermediate-rangeorder.

The films prepared at T_(sub)=45° C. and 400° C. were further examinedwith cross-sectional transmission electron microscopy (TEM), and theimages are shown in FIGS. 2A-2D. No lattice fringes are shown in thehigh-resolution 5 nm-scale TEM images of either film shown in FIGS. 2Aand 2C, confirming that films grown at a high substrate temperatureT_(sub) are equally as amorphous as films grown at lower substratetemperature.

In addition, the low-resolution 50 nm-scale TEM images shown in FIGS. 2Band 2D reveal that both the T_(sub)=45° C. and the T_(sub)=400° C. filmshave a columnar growth structure comprising areas of relatively lowerand higher density inside the film. However, as can be seen from FIG.2D, the high-temperature film has a larger column structure and fewerlow-density regions, as shown by the relatively “bumpy” top edge of thehigh-temperature film as compared to the lower temperature one.Rutherford backscattering (RBS) confirmed that the films grown on ahigh-temperature substrate have a higher density than the lower densityones, showing a density ρ=2.02, 2.14, and 2.18 g/cm³ for the a-Si filmsgrown with T_(sub)=45, 200, and 350° C., respectively, while the twofilms grown with T_(sub)=400° C. exhibited a density ρ=2.17 and 2.22g/cm³. Oxygen resonance RBS also showed a thin oxide layer (1-2 nm) onall films. The oxygen level decreases with increasing depth, but onaverage was measured at 4%, 2%, and 0% oxygen in the films deposited atT_(sub)=45, 200, and 400° C., respectively. These oxygen profiles areconsistent with post-deposition diffusion, whose concentration decreaseswith increasing substrate temperature as the film gets denser andcontains fewer voids.

FIG. 3 reflects the analysis of the specific heat of a-Si films preparedat T_(sub)=45, 200° C., and 400° C. in accordance with the presentinvention.

The specific heat capacity of an amorphous dielectric insulating thinfilm is dependent on temperature as C=aT+bT³, where T is thetemperature, the coefficient “a” is proportional to the density oftunneling states, while the coefficient “b” comes from two differentsources. The first source for the coefficient “b” comes from propagatingphonons in the material, which is a function of Debye temperature andcan be calculated from the elastic properties and mass density of thematerial. Obviously, the specific heat of all solids, amorphous or not,contain such a T³ proportional term. The second source for thecoefficient “b” comes from localized excitations whose origin is notquite understood yet. But it is typical for amorphous solids and it isgenerally accepted as having the same structural origin as do TLS atlower temperatures. These Debye temperatures are calculated from thespeed of sound and mass density measured for each film and are shown inFIG. 3 as “θ_(D1),” “θ_(D2),” and “θ_(D3),” for the films grown atT_(sub)=45, 200, and 400° C., respectively. The contribution to thecoefficient “b” from propagating phonons for each film can then becalculated and is shown in FIG. 3 as the three horizontal lines labeled1, 2, and 3 for the films grown at T_(sub)=45, 200, and 400° C.,respectively.

The values of C/T³ for each of the three amorphous silicon films wereplotted, along with C/T³ for crystalline silicon (c-Si shown as thesolid line) for reference. When analyzed and plotted as C/T³, the y-axisrepresenting specific heat becomes a/T²+b, such that as T rises, a/T²decreases while b remains the same, so C/T³ decreases. As T decreases,a/T² (and C/T³) should increase. However, as can be seen in the plots inFIG. 3, C/T³ for the film prepared at T_(sub)=400° C. does not increasewith decreasing T as much as it does for the films prepared at lowersubstrate temperatures, and even exhibits a decrease for temperaturesbetween about 10 and 40 K, remaining statistically unchanged attemperatures below about 10 K. Since the “a” coefficient is proportionalto the density of tunneling states, this absence of a/T² in C/T³ attemperatures below 10 K for the film prepared at T_(sub)=400° C.indicates that such film has a lower density of tunneling states than dothe films prepared at the higher substrate temperatures.

In addition to the a/T² term which should increase with lower T, therelatively flat parts of the three curves representing the “b”coefficient shown in FIG. 3 are all higher than their correspondingDebye contributions shown by the horizontal lines labeled 1, 2, and 3 asdescribed above, with the difference coming from the localizedexcitations related to TLS. It can be seen that the film deposited atT_(sub)=400° C. exhibits the smallest difference between the flat partsof the curve and the Debye contribution (horizontal line 3), consistentwith such a film having a TLS density lower than that of the otherfilms.

Plots of the internal friction of ˜300 nm-thick a-Si films are shown inFIG. 4. As noted above, TLS exist in almost all amorphous solids, seePohl et al., supra, and thus far have proved difficult to remove. SeeLiu 1997 and Liu 1998, supra. TLS cause elastic dissipation at lowtemperatures and contribute a temperature independent plateau at a fewdegree Kelvin. The internal friction of a typical amorphous solid(a-SiO₂) is shown for reference as a solid line in FIG. 4, while thedouble arrow represents the range of the internal friction plateau ofalmost all amorphous solids. This range, known as the “glassy range,”has been the bottleneck that limits the coherence time ofsuperconducting qubits.

As can be seen from the plots in FIG. 4, the internal friction of a-Sidecreases as the substrate temperature increases. The residual internalfriction in both films with T_(sub)=400° C. comes from the contaminationof our oscillator and is not related to the a-Si films; for a moredetailed explanation, see Liu 2014, supra. Thus the minimum internalfriction of the a-Si films sets an upper limit on the TLS density andcould be lower once the contamination issue can be solved. This is notonly a significant scientific breakthrough but also a crucialbreakthrough for the quantum computing community.

The plots in FIG. 5 show the relative change in the speed of sound ofthe same films shown in FIG. 4, with the relative change measured at thesame time as the internal friction. Accompanied with the internalfriction plateau, amorphous solids also show a linear T-dependentrelative change of speed of sound with a negative slope β at a fewdegree Kelvin. β is proportional to the internal friction plateau. Thiscan be understood as the thermally activated relaxation rate dominatesthe quantum tunneling rate of the same TLS at higher temperatures. SeeS. Rau, C. Enss, S. Hunklinger, P. Neu, and A. Würger, “Acousticproperties of oxide glasses at low temperatures,” Phys. Rev. B 52,7179-7194 (1995). The relative change of speed of sound of a-SiO₂ isalso shown in FIG. 5 as a reference of a typical amorphous solid. As thesubstrate temperature of a-Si films increases, β goes to zero.

All of these experiments confirm that a-Si thin films prepared inaccordance with the present invention exhibit a near-absence of TLS. Inaddition, FIG. 6 shows how the TLS density depends on the mass densityof the a-Si film. The solid symbols are the density of TLS as measuredby specific heat (left y-axis) and the open symbols are the spectraldensity of TLS as measured by internal friction (right y-axis). The massdensity in x-axis is represented by the number of silicon atoms percubic centimeter. The difference between the density and the spectraldensity of TLS lies in the different ways, thus proportion of thestates, been probed by these two measurement techniques. Thus, growthconditions (i.e. growth temperature) that yield amorphous films withhigh mass density will also apply to other amorphous dielectric thinfilms that may be appropriate for use as an insulating layer insuperconducting qubits. Techniques such as (but not limited to)sputtering will likely produce high density films also without TLS aswell. This result may also be extended to other materials such asamorphous silicon nitride (a-SiN), amorphous germanium (a-Ge), andamorphous carbon (a-C). See J. E. Graebner and L. C. Allen, “Thermalconductivity of amorphous germanium at low temperatures,” Phys. Rev. B29, 5626-5633 (1984).

In another exemplary embodiment, the present invention provides a methodfor forming a hydrogen-free amorphous germanium (a-Ge) thin film havingno tunneling states.

In accordance with this embodiment of the present invention, such anamorphous germanium film can be prepared by e-beam deposition from ahigh-purity (99.9999% pure) Ge source on a substrate having a substratetemperature T_(sub) of from about 7.5° C. to just below 200° C. at acontrolled growth rate of about 0.03 to about 0.05 nm/sec. Deposition ismade in an ultra-high vacuum (UHV) environment with a base pressure ofabout 5× 10⁻¹¹ Torr, with the pressure during film growth typicallybeing at about at 5×10⁻⁹ Torr. An a-Ge thin film produced in accordancewith these aspects of the present disclosure can have a thickness ofabout 330 nm and a hydrogen content of less than about 0.1%.

In other embodiments, the a-Ge film can be deposited on the substrateby, sputtering, chemical vapor deposition, or pulsed laser deposition.

The substrate used for growth of such films is typically made of a highpurity silicon wafer having a thickness of about 300 μm. In theexemplary cases illustrated in FIGS. 8 and 9 discussed below, thesubstrate served as the double-paddle oscillator for the internalfriction measurements shown in FIG. 8.

FIG. 7 shows Raman spectra plots of e-beam a-Ge films deposited underthe deposition parameters described above with substrate temperaturesT_(sub) of room temperature (RT) and 120, 160 and 200° C. As can be seenfrom the plots in FIG. 7, only for the film deposited at T_(sub)=200° C.is there a characteristic crystalline peak shown at 300 cm⁻¹, showingthat the film is mostly crystalline. The other films exhibit no suchcrystalline peak, indicating that such films produced at temperaturesbelow 200° C. are amorphous.

It will be noted here that there may be some uncertainty associated withsubstrate temperature. For the Ge film illustrated in FIG. 7, thesubstrate temperature was controlled at 200° C. as controlled bypyrometer which reads directly from the wafer that the substrate wassandwiched in. However, after equilibrium was reached, the substratetemperature showed a reading about 270-280° C. The cause for thisdiscrepancy has not been identified. Consequently it may be possible toconclude that the real substrate temperature was between about 200° C.and 270° C. for the deposition of the Ge film deposited on the nominally200° C. substrate. In any case, since that film was crystallized asshown by the crystalline peak at 300 cm⁻¹, the uncertainty in thesubstrate temperatures above 200° C. does not affect the conclusion ofthis work beyond telling us the experimental boundary for depositingfully amorphous germanium films. As can be readily seen from FIG. 7, forfilms deposited at T_(sub)=7.5, 120, and 160° C., the spectra shows abroad maximum at 240 cm⁻¹ and no sign of crystalline peak at 300 cm⁻¹,indicating the fully amorphous structure of those films.

FIG. 8 shows plots of the internal friction of the four a-Ge filmsdeposited at T_(sub)=7.5, 120, 160, and 200° C. Two-level tunnelingstates (TLS) cause elastic dissipation at low temperatures andcontribute a temperature independent plateau at a few degree Kelvin. Theinternal friction of a typical amorphous solid (a-SiO₂) is shown in FIG.8 (solid line) as a reference. It represents the typical internalfriction plateau one would get from almost all amorphous solids. TLSexist universally in almost all amorphous solids, see Pohl et al.,supra, and have thus far proved difficult to remove, see Liu 1997,supra, and Liu 1998, supra, it has been the bottleneck that limits thecoherence time of superconducting qubits.

FIG. 8 shows that the internal friction of a-Ge decreases as thesubstrate temperature increases. The reduction of internal friction isnot as much as we found earlier in amorphous silicon. But it definitelydemonstrates the same dependence. It is possible that substratetemperature needs a little higher to reduce internal friction further.As deposited germanium film crystallizes at much lower temperature thansilicon, it is a little harder to find the optimal depositiontemperature.

FIG. 9 shows the relative change of speed of sound of the same filmsshown in FIG. 8 measured at the same time with the internal friction.Accompanied with the internal friction plateau, amorphous solids alsoshow a linear T dependent relative change of speed of sound with anegative slope β at a few degree Kelvin. β is proportional to theinternal friction plateau. This can be understood as the thermallyactivated relaxation rate dominates the quantum tunneling rate of thesame TLS at higher temperatures. See Rau et al., supra.

The relative change of speed of sound of a-SiO₂ is also shown in FIG. 8as a reference of a typical amorphous solid. As the substratetemperature of a-Ge films increases, β goes almost to zero.

All of these experiments confirm that TLS can be significantly reducedin a-Ge when properly prepared. Similar to a-Si, a-Ge can also be a goodcandidate to use as a low loss dielectric layer in superconductingquantum bit applications, in particular, when lower substratetemperature is required.

Thus, the present disclosure provides hydrogen-free amorphous dielectricthin Si and Ge films having a near-absence of TLS.

We expect a significant improvement in quantum coherence times by usingfilms prepared in this manner.

In a manner similar to the interaction of TLS with elastic waves whichmodulates the complex elastic constants such that {tilde over(c)}=c₁+ic₂, where the real part c₁ is the elastic constant and theimaginary part c₂ is the elastic dissipation (or internal friction),TLS-carrying electric dipoles can also interact with oscillatingelectric fields and modulate the complex dielectric susceptibility suchthat {tilde over (∈)}=∈+i∈₂, where ∈₁ is the dielectric susceptibilityand ∈₂ is the dielectric dissipation. The relationship between theelastic/acoustic and dielectric properties (see W. A. Phillips,“Two-level states in glasses,” Rep. Prog. Phys. 50, 1657 (1987))suggests that the low TLS contributions to specific heat and internalfriction exhibited by a-Si and a-Ge thin films deposited onhigh-temperature substrates in accordance with the present inventionalso would mean that the TLS contribution to dielectric loss would alsobe minimal.

Thus, we expect that the present invention will provide amorphous thinfilms with the same orders of magnitude reduction of dielectric loss asthe elastic loss found in internal friction for use as an insulatingdielectric. When prepared by electron beam evaporation of the dielectricmaterial on a high-temperature substrate in a high vacuum and at a lowdeposition rate, such films have a high density and a low incidence oftunneling states and that are therefore highly suitable for use as aninsulating dielectric for superconducting quantum bits.

Although particular embodiments, aspects, and features have beendescribed and illustrated, one skilled in the art would readilyappreciate that the invention described herein is not limited to onlythose embodiments, aspects, and features but also contemplates any andall modifications within the spirit and scope of the underlyinginvention described and claimed herein. The present applicationcontemplates any and all modifications within the spirit and scope ofthe underlying invention described and claimed herein, and all suchembodiments are within the scope and spirit of the present disclosure.

What is claimed is:
 1. A process for making a high-density amorphousgermanium dielectric insulating thin film having no two-level tunnelingstates (TLS) for a superconducting circuit, comprising: depositinghydrogen-free amorphous germanium on a substrate having a substratetemperature T_(sub) between about 7.5° and 200° C., the hydrogen-freeamorphous germanium being deposited in an ultra-high vacuum systemhaving a base pressure of about 5×10⁻¹¹ Torr and at a deposition vacuumpressure of about 5×10⁻⁹ Torr, the deposition taking place at acontrolled deposition rate of about 0.03 to about 0.05 nm/s; wherein thesubstrate temperature, vacuum pressure, and deposition rate areconfigured to cause the hydrogen-free amorphous germanium to not becomecrystalline but to remain in its amorphous state to form a TLS-freeamorphous germanium silicon dielectric insulating thin film having adensity close to that of its crystalline counterpart.
 2. The processaccording to claim 1, wherein the amorphous germanium is deposited onthe substrate by electron beam evaporation, sputtering, chemical vapordeposition, or pulsed laser deposition.
 3. A product made by the processof claim
 1. 4. A method for making a Josephson junction with ahigh-density amorphous germanium dielectric insulating thin film havingno two-level tunneling states (TLS), comprising: depositing a firstsuperconducting material layer on a substrate; depositing hydrogen-freeamorphous germanium on the first superconducting material layer, thehydrogen-free amorphous germanium being deposited with a substratetemperature between 7.5° and 200° C. under a high vacuum pressure ofabout 5×10⁻⁹ Torr and at a controlled deposition rate of about 0.03 toabout 0.05 nm/s; and depositing a second superconducting material layeron the amorphous germanium dielectric insulating thin film; wherein thesubstrate temperature, vacuum pressure, and deposition rate areconfigured to cause the hydrogen-free amorphous germanium to not becomecrystalline but to remain in its amorphous state to form a TLS-freeamorphous germanium thin film having a density close to that of itscrystalline counterpart; wherein the amorphous germanium thin filmcomprises an insulating dielectric layer separating the first and secondsuperconducting material layers.
 5. The process according to claim 4,wherein the hydrogen-free germanium is deposited on the substrate byelectron beam evaporation, sputtering, chemical vapor deposition, orpulsed laser deposition.
 6. A product made by the process of claim 4.